Optical Mellin transform through Haar wavelet transformation

A novel method for performing the 2D all-optical Mellin transform is suggested. It is shown that the coordinates of an image can be converted from a linear scale to a logarithmic scale through a Haar wavelet transform followed by an inverse logarithmic Haar wavelet transform and an optical system is proposed for the implementation of this process. Compared with existing methods the new method is exact in the sense that it imposes no additional restrictions to the input image. High accuracy can be achieved by using high-order wavelets.